An Analytical Approach towards Passive Ferromagnetic Shimming Design for a High-Resolution NMR Magnet

This paper presents a warm bore ferromagnetic shimming design for a high resolution NMR magnet based on spherical harmonic coefficient reduction techniques. The passive ferromagnetic shimming along with the active shimming is a critically important step to improve magnetic field homogeneity for an NMR Magnet. Here, the technique is applied to an NMR magnet already designed and built at the MIT's Francis Bitter Magnet Lab. Based on the actual magnetic field measurement data, a total of twenty-two low order spherical harmonic coefficients is derived. Another set of spherical harmonic coefficients was calculated for iron pieces attached to a 54 mm diameter and 72 mm high tube. To improve the homogeneity of the magnet, a multiple objective linear programming method was applied to minimize unwanted spherical harmonic coefficients. A ferromagnetic shimming set with seventy-four iron pieces was presented. Analytical comparisons are made for the expected magnetic field after Ferromagnetic shimming. The theoretically reconstructed magnetic field plot after ferromagnetic shimming has shown that the magnetic field homogeneity was significantly improved.